434 Prof. Thomson on the Dynamical Theory of Heat. 



be kept in all points at a uniform temperature t. Then taking 

 ^, 6, i/r to denote the thermo-electric powers of bars of the sub- 

 stance cut from directions parallel to the edges of the parallele- 

 piped, quantities which would be equal to one another in what- 

 ever directions those edges are if the substance were non-cry- 

 stalline ; and 6', 6", cf)', (j>", -yfr', ■\Jr" other elements depending on 

 the nature of the substance with reference to the directions of 

 the sides of the parallelopiped, to which the name of thermo- 

 electric obliquities may be given, and which must vanish for 

 every system of rectangular planes through the substance if it 

 be non-crystalline, we may assume the following expression for 

 the reversible thermal effects of the cui'rent : — 



Q,,^^^=bcj{he+i<i>"+jf') 



Q^c,a) = caj-{hd' + i<f>+jylr") i> ... (31)^ 

 Q(a,6)=abj{he" + icp'+jylr)j 



where Q(i,c), Qic,a), Q(o,i) denote quantities of heat absorbed per 

 second at the sides by which positive current components enter, 

 or quantities evolved in the same time at the opposite sides. 

 Hence if the opposite sides be kept at different temperatures, 

 currents will pass, unless prevented by the resistance of surround- 

 ing matter ; and the electromotive forces by which these currents 

 are urged in directions parallel to the three edges of the paral- 

 lelopiped have the following expressions, in which ua, vb, and wc 

 denote the difference of temperature between corresponding 

 points in the pairs of sides be, ca, and ab respectively reckoned 

 positive, when the temperature increases in the direction of posi- 

 tive components of current : — 



'¥ = -b{u<l>" + vc\> + i>i<h') I . . . (32). 

 G = — C (m-v/t' -i- t;-»|r" -f- iv^) J 



The negative signs are prefixed, in order that positive values of 

 the electromotive components may correspond to forces in the 

 direction assumed for positive components of current. 



158. The most general conceivable elementary type of crystal- 

 line thermo-electnc properties is expressed in the last equations, 

 along with the equations (31) by which we arrived at them ; and 

 we shall see that every possible case of thermo-electric action in 

 solids of whatever kind may be investigated by using them with 

 values, and variations it may be, of the coefficients (p, 6, &c.. 



